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www.cmr.no Interactive computation and visualization of wind farm flow fields based on model reduction Visual Computing Forum 04/11/2011 1 Yngve Heggelund CMR Computing

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www.cmr.no Visual Computing Forum 04/11/2011 2 Norwegian Centre for Offshore Wind Energy - NORCOWE Center for environment-friendly energy research (CEER) 50% RCN, the rest from industry and research partners Combining Norwegian offshore technology and Danish wind energy competence Research partners: Christian Michelsen Research AS (host) UiS UiA UiB Aalborg University Uni Research AS

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www.cmr.no NORCOWE WP 4 – Wind farm optimization nVision: Model system for optimizing the layout of (offshore) wind farms based on Computational Fluid Dynamics (CFD) nNowcasting: 2-120 seconds nPower system integration nWind farm modelling Visual Computing Forum 04/11/2011 3

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www.cmr.no Visual Computing Forum 04/11/2011 4 Wakes nWake effects caused by upstream turbines nReduces energy output of downstream turbines nIncreases material fatigue because of increased turbulence

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www.cmr.no Visual Computing Forum 04/11/2011 5 Objectives nFind a layout which minimizes the wake effects nReduce the uncertainty of production estimates

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www.cmr.no Visual Computing Forum 04/11/2011 6 Motivation nTraditional approach: simplified wake models nOften underestimates wake effects nCFD provides the state-of-the-art method for solving complex flow problems nCFD is computationally expensive – one simulation typically takes hours/days/weeks to complete nProhibits straightforward use in optimization of layout nWe have to make some simplifications!

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www.cmr.no Model reduction, background nIdea: Restrict the solution space to a reduced representative subspace nFull dimension ~3 000 000 grid cells nSubspace dimension ~100 unknowns nE.g. used for real-time visualization of fluid effects (Treuille et al. 2006) nExamples of other applications of model reduction for fluids nStudy of flow past a rectangular cavity (Rowley, 2002) nOptimal rotary control of cylinder wake (Bergman et al., 2005) Visual Computing Forum 04/11/2011 7

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www.cmr.no Model reduction, theoretical framework Visual Computing Forum 04/11/2011 8

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www.cmr.no Model reduction, operator examples Visual Computing Forum 04/11/2011 9 CFD discretization Reduced order space representation

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www.cmr.no Contructing a representative basis nSnapshots of CFD solutions for different placements of turbines nSingular value decomposition (SVD) to extract an orthonormal basis which minimizes the reconstruction error A representative basis is critical for a good result! Visual Computing Forum 04/11/2011 10

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www.cmr.no Tiles nMust be able to move turbines nConstruct tiles which capture localized behaviour, which can be assembled at runtime nCouple tiles through matching the boundary conditions nResults in a system of equations represented by a large sparse block matrix nSolving for the coefficients in each tile nTrade-off between matching boundary conditions and fulfilling the steady state RANS equations Visual Computing Forum 04/11/2011 11

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www.cmr.no Test case nIdealized system with three wind turbines and wind predominantly from the west nWhere should turbine C be placed? n6 simulations with FLACS-Wind (CMR GexCon) for different positions of the back row turbine Visual Computing Forum 04/11/2011 12 A B C The two most important modes in the basis

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www.cmr.no Interactive tool for testing turbine positions nUser can move turbines by dragging tiles nNew flow fields and production estimates are calculated within seconds Visual Computing Forum 04/11/2011 13

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www.cmr.no Demo Visual Computing Forum 04/11/2011 14

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